
The partition function
is invariant under area-preserving diffeomorphisms of the Riemann
surface \(\Sigma \) , and so depends on \(e\)  and the metric of \(\Sigma \)  only through the combination
\(e^2\,a\)  [1]}, [2]}. It is therefore possible
to set \(e=1\)  without loss of generality and consider all amplitudes of the gauge theory as functions of the
area \(a\) . In this sense two-dimensional Yang-Mills theory is a mild
variant of a topological field theory that is an
example of an `area-dependent quantum field theory'.
